GRE Smart Books with Neil: A Mind for Numbers: How to Excel at Math and Science (Even if you Flunked Algebra) by Barbara Oakley

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Manhattan Prep GRE Instructor Neil Thornton - Book Reviews to Ace the Test

Can’t get enough of Neil’s GRE wisdom? Few can. Fortunately, you can join him twice monthly for a free hour and a half study session in Mondays with Neil.


As a long-time instructor of all things standardized testing (GRE, GMAT, LSAT, SAT), I love reading books about math, logic, learning, skill acquisition, neurology, and psychology. Is important to me to stay up-to-date with anything that will help my students use their study time effectively. In this blog series, I’ll be bringing you book reviews and recommendations, as well as excerpts and summaries you can put into practice right away on your GRE journey.

I really like Barbara Oakley’s A Mind for Numbers: How to Excel at Math and Science (Even if you Flunked Algebra). I recommend it to anyone starting his or her GRE journey, and anyone stuck, frustrated, or overwhelmed by a big stack of GRE books and limited time. Even though A Mind for Numbers has math and science in its title, it’s really about learning any subject or skill. With little effort, you can apply Oakley’s lessons to both Quant and Verbal on the GRE or pretty much any subject–even outside physical or creative efforts.

What you won’t get in this book

You won’t get specific math lessons. Oakley occasionally hints at math and science concepts, but usually to illustrate a point about how to create Mnemonic devices or structure your study. A Mind for Numbers is more of a user’s manual for whatever textbook you happen to have in front of you. You’ll find that her book dovetails very neatly with our ManhattanPrep Strategy guides, for instance, or any book that illustrates a concept with problem sets at the end of every chapter.

What you will get in this book

You will get some very clear, actionable lessons about learning: structuring your study, creative problem solving, building your memory, and overcoming procrastination. At first, you may be a little skeptical about some of the analogies she uses (Pinball Machine? Brain Octopus? Zombies?) but Oakley, to her credit, has done her homework and backs up her ideas with the latest published research. [Too often, books about learning are full of clever-sounding ideas that have no basis in empirical science. Remember that trend about “visual” vs. “kinesthetic” learners? It turned out to be unscientific bunk.]

If you’ve always been good at studying and learning, you can get away with sticking to GRE-specific material, but if you’ve ever struggled with learning or if you’re prone to procrastination, this is a great book for you. I wish I’d read this book when I was in 8th grade. I might have had a much easier time in high school.

Focus vs. Diffuse Mode

Here’s a cool concept that you can use from the book: In the opening chapters, Oakley makes a great distinction between two modes of thinking, which she terms “focused” and “diffuse” modes. “Focus mode” is the kind of thinking you do when you study intently — when you really zoom in to solve GRE problems, especially on test day. According to Oakley, “Focused-mode thinking is essential for studying math and science. It involves a direct approach to solving problems using rational, sequential, analytical approaches.”

Too often, though, you may find yourself stuck on a problem, unable to see the solution no matter how hard you focus. You may be focusing too much, and suffering from the “Einstellung effect.” Oakley writes, “In this phenomenon, an idea you already have in mind, or your simple initial thought, prevents a better idea or solution from being found.” I see this all too often with my GRE students, they are so focused on the first idea they havethat they miss far easier and effective methods to solve tough problems.

Therefore, you may need to switch into “Diffuse Mode” thinking. This is the kind of thinking you do when you’re not thinking—the unconscious processes that go on when you’re sleeping, taking a shower, or doing the dishes. According to Oakley, “Diffuse-mode thinking is also essential for learning math and science. It allows us to suddenly gain a new insight on a problem we’ve been struggling with and is associated with ‘big-picture’ perspectives. Diffuse-mode thinking is what happens when you relax your attention and just let your mind wander.” When you’re studying for the GRE, switching into diffuse mode is easy: Take a break. Fold some laundry. Go to bed. Leave a problem unsolved (don’t check that answer) and come back to it later, even tomorrow. You’ll be shocked at how often the solution will be there even if you don’t directly think about it. (The analogy is something about letting the bumpers on your mental pinball machine spread out so the ball can bounce to more areas of the brain.)

On GRE test day, engaging “diffuse mode” is essential, but very hard to do when all you want to do is focus and focus harder. In my experience, there are a couple of ways to let the unconscious diffuse mode do the work without wasting time. One method is to read the whole problem over, and then ignore it for a few seconds while you do the mindless “busy” work of setting up your scratch paper, copying essential numbers from the problem, drawing diagrams and figures, labeling your units, etc. By the time you get around to focusing, you may get some insight into the problem that you might have missed if you started focusing too early. Another great way to engage the diffuse mode is when you’re stuck half-way through a problem: “mark” the question, make a random guess, and move on. Come back to it a few minutes later. If you’re blocked and stuck in the Einstellung effect, no amount of focus is going to get you out of it, you must move on. Again, amazing things happen when you’re not consciously working on a problem. (Practice this “mark and move” approach often while you’re doing your GRE study, by the way.)

In future articles, I’ll dig more into other great advice Oakley offers. In the meantime, I’d love to hear from you. How do you switch back and forth between focused and diffuse mode? Leave your thoughts in the comments below. 📝


Find Neil’s musings helpful? Most do. Don’t forget that you can join him twice monthly for a free hour and a half study session in Mondays with Neil.


neil-thornton-manhattan-prep-gre-instructorWhen not onstage telling jokes, Neil Thornton loves teaching you to beat the GRE and GMAT. Since 1991, he’s coached thousands of students through the GRE, GMAT, LSAT, MCAT, and SAT, and trained instructors all over the United States. He scored 780 on the GMAT, a perfect 170Q/170V score on the GRE, and a 99th percentile score on the LSAT. Check out Neil’s upcoming GRE course offerings here or join him for a free online study session twice monthly in Mondays with Neil.

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